Ice is added to 0.75 L of water at 20°C to make very cold water at 0°C. If enough 0°C ice is added so that the mixture becomes all liquid, how much liquid is in the pitcher when this occurs? Density of water = 1.00 x 103 kg/m3.
For water
Q = mc(Tf-Ti) (I don't know the specific heat of water offhand, get the mass using density). This must be equal to the heat required to melt the ice: Q = mL (don't know the latent heat of fusion for water either. Solve for mass of ice, use density to find volume, add to original .75liters.
To solve this problem, we need to determine the amount of ice that is required to lower the temperature of the water from 20°C to 0°C, and then calculate the resulting volume of liquid after all the ice has melted.
First, let's calculate the mass of the water in the pitcher:
Mass = Density x Volume
Since the density of water is given as 1.00 x 10^3 kg/m^3 and the volume is 0.75 L, we can convert the volume to cubic meters:
Volume = 0.75 L = 0.75 x 10^-3 m^3
Now we can calculate the mass of the water:
Mass of water = 1.00 x 10^3 kg/m^3 x 0.75 x 10^-3 m^3 = 0.75 kg
Next, let's calculate the amount of heat that needs to be lost by the water to cool it from 20°C to 0°C. We can use the specific heat capacity of water, which is approximately 4.18 J/g°C:
Heat lost = Mass x Specific heat capacity x Temperature change
The mass of the water is 0.75 kg and the temperature change is 20°C - 0°C = 20°C, so we can calculate the heat lost:
Heat lost = 0.75 kg x 4.18 J/g°C x 20°C = 62.7 J
Now, let's calculate the amount of heat that can be absorbed by the ice to melt it at 0°C without changing its temperature. The specific latent heat of fusion for ice is approximately 334 J/g:
Heat absorbed by ice = Mass of ice x Specific latent heat of fusion
Since the ice is at 0°C, which is the same temperature as the water, we need to determine the mass of ice that can absorb 62.7 J of heat:
Mass of ice = Heat absorbed by ice / Specific latent heat of fusion
Mass of ice = 62.7 J / 334 J/g ≈ 0.187 g
Finally, let's calculate the resulting volume of liquid when all the ice has melted. Since the density of water is 1.00 x 10^3 kg/m^3, we can calculate the volume of the liquid using the mass of the ice melted:
Volume of liquid = Mass of ice melted / Density
Volume of liquid = 0.187 g / (1.00 x 10^3 kg/m^3) = 0.187 x 10^-3 m^3 = 0.187 mL
Therefore, when all the ice has melted, the resulting volume of liquid in the pitcher will be approximately 0.187 mL.